where \(i\)  and \(j\)  denote the micromagnetic cells, and \(p\) , \(q\)  represent the Cartesian components of the thermal field. \(T_{i}\)  and \(\alpha _i\)  are respectively temperature and the Gilbert damping at cell \(i\) , and \(a\)  is the cell size. \(k_\text{B}\)  is the Boltzmann constant [1]}. The numerical results presented in this study are averaged over 15 random configurations.
